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Simplifying 0 = 25x2 + -3x + -13 Reorder the terms: 0 = -13 + -3x + 25x2 Solving 0 = -13 + -3x + 25x2 Solving for variable 'x'. Combine like terms: 0 + 13 = 13 13 + 3x + -25x2 = -13 + -3x + 25x2 + 13 + 3x + -25x2 Reorder the terms: 13 + 3x + -25x2 = -13 + 13 + -3x + 3x + 25x2 + -25x2 Combine like terms: -13 + 13 = 0 13 + 3x + -25x2 = 0 + -3x + 3x + 25x2 + -25x2 13 + 3x + -25x2 = -3x + 3x + 25x2 + -25x2 Combine like terms: -3x + 3x = 0 13 + 3x + -25x2 = 0 + 25x2 + -25x2 13 + 3x + -25x2 = 25x2 + -25x2 Combine like terms: 25x2 + -25x2 = 0 13 + 3x + -25x2 = 0 Begin completing the square. Divide all terms by -25 the coefficient of the squared term: Divide each side by '-25'. -0.52 + -0.12x + x2 = 0 Move the constant term to the right: Add '0.52' to each side of the equation. -0.52 + -0.12x + 0.52 + x2 = 0 + 0.52 Reorder the terms: -0.52 + 0.52 + -0.12x + x2 = 0 + 0.52 Combine like terms: -0.52 + 0.52 = 0.00 0.00 + -0.12x + x2 = 0 + 0.52 -0.12x + x2 = 0 + 0.52 Combine like terms: 0 + 0.52 = 0.52 -0.12x + x2 = 0.52 The x term is -0.12x. Take half its coefficient (-0.06). Square it (0.0036) and add it to both sides. Add '0.0036' to each side of the equation. -0.12x + 0.0036 + x2 = 0.52 + 0.0036 Reorder the terms: 0.0036 + -0.12x + x2 = 0.52 + 0.0036 Combine like terms: 0.52 + 0.0036 = 0.5236 0.0036 + -0.12x + x2 = 0.5236 Factor a perfect square on the left side: (x + -0.06)(x + -0.06) = 0.5236 Calculate the square root of the right side: 0.723602101 Break this problem into two subproblems by setting (x + -0.06) equal to 0.723602101 and -0.723602101.Subproblem 1
x + -0.06 = 0.723602101 Simplifying x + -0.06 = 0.723602101 Reorder the terms: -0.06 + x = 0.723602101 Solving -0.06 + x = 0.723602101 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.06' to each side of the equation. -0.06 + 0.06 + x = 0.723602101 + 0.06 Combine like terms: -0.06 + 0.06 = 0.00 0.00 + x = 0.723602101 + 0.06 x = 0.723602101 + 0.06 Combine like terms: 0.723602101 + 0.06 = 0.783602101 x = 0.783602101 Simplifying x = 0.783602101Subproblem 2
x + -0.06 = -0.723602101 Simplifying x + -0.06 = -0.723602101 Reorder the terms: -0.06 + x = -0.723602101 Solving -0.06 + x = -0.723602101 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.06' to each side of the equation. -0.06 + 0.06 + x = -0.723602101 + 0.06 Combine like terms: -0.06 + 0.06 = 0.00 0.00 + x = -0.723602101 + 0.06 x = -0.723602101 + 0.06 Combine like terms: -0.723602101 + 0.06 = -0.663602101 x = -0.663602101 Simplifying x = -0.663602101Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.783602101, -0.663602101}
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